相关论文: Statistical Cryptography using a Fisher-Schr\"{o}d…
A novel strategy to encrypt covert information (code) via unitary projections into the null spaces of ill-conditioned eigenstructures of multiple host statistical distributions, inferred from incomplete constraints, is presented. The host…
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which…
The statistical distribution, when determined from an incomplete set of constraints, is shown to be suitable as host for encrypted information. We design an encoding/decoding scheme to embed such a distribution with hidden information. The…
The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction, it is crucial to select data that are sensitive to the…
This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its "quality". Identification can be regular or irregular, depending on whether the Fisher information for…
A robust prediction model invoking the Takens embedding theorem, whose \textit{working hypothesis} is obtained via an inference procedure based on the minimum Fisher information principle, is presented. The coefficients of the ansatz,…
Privacy-preserving instance encoding aims to encode raw data as feature vectors without revealing their privacy-sensitive information. When designed properly, these encodings can be used for downstream ML applications such as training and…
The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM…
The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted…
We present two new statistical machine learning methods designed to learn on fully homomorphic encrypted (FHE) data. The introduction of FHE schemes following Gentry (2009) opens up the prospect of privacy preserving statistical machine…
The problem of determining the achievable sensitivity with digitization exhibiting minimal complexity is addressed. In this case, measurements are exclusively available in hard-limited form. Assessing the achievable sensitivity via the…
The problem of determining the intrinsic quality of a signal processing system with respect to the inference of an unknown deterministic parameter $\theta$ is considered. While the Fisher information measure $F(\theta)$ forms a classical…
Learning an encoding of feature vectors in terms of an over-complete dictionary or a information geometric (Fisher vectors) construct is wide-spread in statistical signal processing and computer vision. In content based information…
Privacy is under threat from artificial intelligence revolution fueled by unprecedented abundance of data. Differential privacy, an established candidate for privacy protection, is susceptible to adversarial attacks, acts conservatively,…
We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to…
Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for…
We study here the difference between quantum statistical treatments and semi-classical ones, using as the main research tool a semi-classical, shift-invariant Fisher information measure built up with Husimi distributions. Its semi-classical…
In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different…
We present the first prediction of the probability distribution function (PDF) for self-organization of shear flows modeled by a nonlinear diffusion equation with a stochastic forcing. A novel non-perturbative method based on a coherent…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…